# Questions tagged [bivariate-distributions]

For questions on bivariate distribution, the joint probability distribution of two random variables.

297 questions
Filter by
Sorted by
Tagged with
38 views

74 views

### Why is the following variable a mixed random variable?

Let X∼N(0,1) and W∼Bernoulli(1/2) be independent random variables. Define the random variable Y as a function of X and W: Find the PDF of Y and X+Y. I don't understand why Z turned out to be a mixed ...
• 3
1 vote
43 views

### Bivariate normal CFD approximation using characteristic function

The normal distribution CFD can be approximated using $$F_X (x)=P[X≤x]=\frac{1}{2}-\frac{1}{π} \int^{\infty}_{0}\operatorname{Re}\left[\frac{e^{-iux}\phi_X (u)}{iu}\right]du$$ where the characteristic ...
• 13
105 views

### The root of the sum of two normally distributed variables

Given $X,Y \sim \mathcal{N}(0,1)$ and $Z=\sqrt{X^2 + Y^2}$, find the PDF of $Z$. I know from digging around that this will follow a Rayleigh distribution since the sum of two squared normally ...
• 31
1 vote
47 views

• 135
1 vote
207 views

### Covariance for a bivariate normal distribution

I have a question concerning the bivariate normal distribution where I have been able to prove that the first covariance we are asked for is equal to $0$, but was not sure if this would be implying ...
• 535
1 vote